combined effects of climate, predation, and density

Ecological Applications, 25(6), 2015, pp. 1606–1617� 2015 by the Ecological Society of America

Combined effects of climate, predation, and density dependenceon Greater and Lesser Scaup population dynamics

BETH E. ROSS,1,7 MEVIN B. HOOTEN,2,3,4 JEAN-MICHEL DEVINK,5 AND DAVID N. KOONS6

1Department of Wildland Resources, Utah State University, Logan, Utah 84322 USA2U.S. Geological Survey, Colorado Cooperative Fish and Wildlife Research Unit, Fort Collins, Colorado 80523 USA

3Department of Fish, Wildlife, and Conservation Biology, Colorado State University, Fort Collins, Colorado 80523 USA4Department of Statistics, Colorado State University, Fort Collins, Colorado 80523 USA

5Stantec Consulting, Inc., Saskatoon, Saskatchewan S7K0K3 Canada6Department of Wildland Resources and the Ecology Center, Utah State University, Logan, Utah 84322 USA

Abstract. An understanding of species relationships is critical in the management andconservation of populations facing climate change, yet few studies address how climate altersspecies interactions and other population drivers. We use a long-term, broad-scale data set ofrelative abundance to examine the influence of climate, predators, and density dependence onthe population dynamics of declining scaup (Aythya) species within the core of their breedingrange. The state-space modeling approach we use applies to a wide range of wildlife species,especially populations monitored over broad spatiotemporal extents. Using this approach, wefound that immediate snow cover extent in the preceding winter and spring had the strongesteffects, with increases in mean snow cover extent having a positive effect on the local surveyedabundance of scaup. The direct effects of mesopredator abundance on scaup populationdynamics were weaker, but the results still indicated a potential interactive process betweenclimate and food web dynamics (mesopredators, alternative prey, and scaup). By consideringclimate variables and other potential effects on population dynamics, and using a rigorousestimation framework, we provide insight into complex ecological processes for guidingconservation and policy actions aimed at mitigating and reversing the decline of scaup.

Key words: Aythya affinis; Aythya marila; climate change; density dependence; Greater Scaup; LesserScaup; Northwest Territories, Canada; population dynamics; predators; trophic interactions.

INTRODUCTION

Climate change is occurring more rapidly than during

past global warming cycles (Rahmstorf et al. 2007), and

worst-case scenarios predict a loss of biodiversity that

would constitute the sixth major extinction (Bellard et

al. 2012). Yet few studies address how climate alters

species interactions (e.g., competition, predation), and

shift resulting population dynamics (Rockwell et al.

2011, Zarnetske et al. 2012). Without fully understand-

ing how climate affects populations in parallel with

species interactions and other population drivers,

effective management and conservation in the era of

global climate change will be difficult (Hulme 2005).

In addition to direct effects on populations, e.g.,

through thermoregulatory effects on demography,

climate can indirectly affect populations via changes to

food web dynamics (Russell and Ruffino 2012) through

predator–prey interactions (Wilmers et al. 2007) or

resource availability (McCaffery et al. 2012). Moreover,

changes in climate can intensify mechanisms related to

density dependence (e.g., intraspecific competition,

disease transmission, prey switching; Lima and Berry-

man 2006). While work on small mammals (Lima et al.

2002) and ungulates (Forchhammer et al. 2002) has

highlighted the interaction of density dependence,

climate, and predation, many studies on population

dynamics fail to incorporate multiple drivers into

population models. Rarely are density dependence,

climate, and trophic interactions examined simulta-

neously, which can lead to spurious conclusions about

the mechanisms affecting population dynamics (Vilju-

grein et al. 2005).

In this paper, we use a long-term, broad-scale

abundance data set of Lesser Scaup (Aythya affinis)

and Greater Scaup (Aythya marila), which are combined

during surveys because of their similar appearance, to

evaluate the influence of climate variables, indices of

predator abundance, and density dependence on scaup

population dynamics in the western boreal forest of

Canada, the core of their breeding range. Scaup in

North America have declined to levels that are ;8%

below the long-term average, an average that declines

with the trajectory of the population (Zimpfer et al.

2014). The most precipitous declines have occurred in

their preferred western boreal forest habitat in Canada

(Ross et al. 2012, Zimpfer et al. 2014). Although there is

not a consensus on the underlying mechanisms causing

Manuscript received 26 March 2014; revised 26 November2014; accepted 18 December 2014; final version received 28January 2015. Corresponding Editor: E. F. Zipkin.

7 E-mail: [email protected]

1606

the population decline (Austin et al. 2006), climate

seems to be playing an important role (Drever et al.

2012), but an understanding of how climate, predation,

and density dependence drive population dynamics is

lacking.

We propose, and test, several possible drivers of the

scaup decline in their core breeding range. The effects of

climate, for example, could directly affect waterfowl

populations through a decrease in wetland abundance

and quality via increased drought (Fig. 1; Sorenson et al.

1998). In fact, some of these changes may already be

occurring. Decreasing winter snow cover duration on

the boreal breeding grounds is related to reduced

regional scaup population growth rates, presumably

through impacts on summer wetland availability and

quality for breeding scaup (Drever et al. 2012). In

addition to direct effects on wetland habitat and

associated food resources, climate could also alter

predation on scaup through changes in alternative prey

(Fig. 1). If predators preferentially feed on alternative

prey species (e.g., small mammals) rather than a focal

species (e.g., scaup), changes in climate can result in

indirect effects on the focal species through changes in

the alternative prey and a shared predator response to

those resources (e.g., apparent competition; Oliver et al.

2009). For example, if predators experience increased

survival and fecundity from an abundance of small

mammals in year t, scaup would be negatively impacted

through increased predation in year tþ 1. In such cases,

we might expect lagged temporal effects of climate on a

focal species, because it can take time for numerical and

functional responses to percolate through a food web

(Walker et al. 2013). It is worth noting, however, that

the effect of increased predators would only be expected

if there were a shortfall in primary prey, and that the lag

effects on scaup might be felt two years later if delayed

breeding occurs.

Through direct interactions with the predator com-

munity, an increased predator abundance should

negatively affect the abundance of a focal prey species

via increased prey mortality, but handling time and prey

switching can mitigate the intensity of such effects (van

Leeuwen et al. 2013). Both climate and predation can

thus change the density of a focal population through a

number of non-mutually exclusive trophic interactions.

In turn, these effects should adjust the strength and

ability to detect the presence of density dependence

(Turchin 2003, Viljugrein et al. 2005).

Given the precipitous decline of the once-abundant

North American scaup population, and evidence that

climate may be playing a role in this decline (Drever et

al. 2012), our objective was to simultaneously address

how density dependence, climate, and predators all

affect scaup population dynamics at the core of their

breeding range. To better elucidate how these factors

influence the dynamics of this declining species, we used

a state-space modeling approach that controls for

observation error (de Valpine and Hastings 2002), the

latter of which can lead to erroneous conclusions about

the impact of density dependence and environmental

variation on population dynamics (Freckleton et al.

2006, Lebreton and Gimenez 2013). By simultaneously

considering climate variables and other potential drivers

of population dynamics, and using a rigorous estimation

framework, future research and management can be

based on more robust science for guiding conservation

and policy decisions aimed at mitigating and reversing

the deleterious response of scaup and other species.

METHODS

Survey methods

Every year since 1955, the U.S. Fish and Wildlife

Service and Canadian Wildlife Service conduct the

North American Waterfowl Breeding Population and

Habitat Survey (BPOP), which provides a rich source of

demographic data for .10 duck species, including

scaup. The BPOP includes over 3.3 million km2 in the

north-central United States, much of western Canada,

and Alaska; purposefully covering a large portion of

each species’ breeding range (Fig. 2; see Zimpfer et al.

2014). Surveys are conducted every May through June

using aerial transects (Smith 1995), and flown at 145–

170 km per hour at an altitude of 30–50 m. Multiple 28.8

3 0.4 km segments are combined to form strata, the

main spatial unit of the survey defined by ecozones and

political boundaries. Observers survey 200 m on each

side of the segment and record by species the number of

lone males, flocked males (two or more), pairs, mixed-

sex groups (three or more), but not lone females. Our

focus was on the delineation of scaup recorded as

breeding pairs, rather than total scaup abundance,

because pairs best represent the breeding potential of

the population. We did not use data regarding single

males because the skewed sex ratio in scaup means that

males are not limiting in the population (Afton and

Anderson 2001), and scaup have not started breeding

FIG. 1. Proposed direct and indirect drivers affecting scaup(Aythya spp.) on their breeding grounds. Dotted arrows andovals indicate hypothesized indirect mechanisms influencingpopulation drivers incorporated into the model, solid arrowsindicate direct effects, and dashed arrows indicate interactionsbetween effects.

September 2015 1607SCAUP POPULATION DYNAMICS

when some surveys are conducted; therefore, lone males

are not necessarily indicative of breeding pairs. We

chose the Northwest Territories region of Canada

(NWT) because of the substantial declines in regional

scaup abundance (Afton and Anderson 2001, Ross et al.

2012) and the nature of available data regarding

predators. Pelt harvest in this territory is conducted

more for subsistence trapping, and the trends of

furbearer harvest probably are more reflective of true

furbearer demography than in other territories and

states where trapping has become more recreational.

Model for population dynamics

Our statistical model for the scaup population in the

NWT is motivated by Gompertz density dependence

(Turchin 2003, Dennis et al. 2006). Under discrete-time

Gompertz growth, the population at time t (Nt) is

defined mathematically as

Nt ¼ kNht�1 ð1Þ

where k is the population growth rate and h represents

density dependence in the system. Taking the log of both

sides and incorporating a term for stochasticity (e) yields

logðNtÞ ¼ zt ¼ r þ hzt�1 þ et ð2Þ

where r¼ log(k), the rate of population growth from low

density (N¼ 1) and h is the effect of dependence on the

log of population size at time t � 1 (zt�1). In the

Gompertz model, r takes on additional meaning because

it also influences the carrying capacity. Dennis et al.

(2006) provide closed-form solutions to the stationary

equilibrium of a stochastic Gompertz model, conditional

on estimates of r, h, e, and even homogenous covariates.

For time-varying covariates, however, there are no

closed-form solutions to the stationary equilibrium.

Moreover, equilibria are undefined when temporal

variation in covariates is nonstationary (i.e., changing

mean, variance, or both), but in such instances the

stochastic Gompertz model is still quite useful for

examining the effects of density dependence and

exogenous variables on population dynamics over a

defined period of time.

Our basal unit of data was the total number of

recorded scaup pairs, yj,t, summed across segments in

stratum j in year t. The BPOP scaup data are over-

dispersed and contain a disproportionately high number

of zeros at the stratum level relative to a Poisson

distribution (Ver Hoef and Boveng 2007, Ross et al.

2012). Thus, we considered two potential data models

for statistical estimation of population dynamics, a

model where yj,t ; NegBinom(l j,t, /), with the

parametrization of the negative binomial where E(yj,t)

¼ lj,t and var(yj,t) ¼ lj,t þ /l2j;t, and a zero-inflated

negative binomial model where

yj;t ;0; with probability wNegBinomðlj;t;/Þ; with probability ð1� wÞ

�

ð3Þ

for stratum j ¼ 1, . . . , m during observation period t ¼1, . . . , T (e.g., years 1957–2012). The lj,t parameter is

thus related to the underlying number of pairs in

stratum j and year t, and / is an overdispersion

parameter. The overdispersion parameter accounts for

extra heterogeneity in the data, and when / . 10, the

negative binomial model approximates a Poisson

distribution (Bolker 2007, Ver Hoef and Boveng 2007)

The parameters related to the error associated with the

observation model, w and /, account for random

under- and overcounting, but do not account for any

systematic bias in the counts. Although there probably

FIG. 2. Traditional study area for the North American Waterfowl Breeding Population and Habitat Survey (BPOP). The areafor the Northwest Territories portion of the study is shown in solid black and includes strata 13 through 18, covering ;713 000km2.

BETH E. ROSS ET AL.1608 Ecological ApplicationsVol. 25, No. 6

are measurable variables associated with the observation

process that may cause changes in the error associated

with this model, our method for model implementationdoes not currently allow for the incorporation of such

models, and custom-built models are the focus of future

research efforts.Using lj,t from the data model (Eq. 3), the process

model was specified as

zj;t ¼ logðlj;tÞ ¼ b0; j þ hzj;t�1 þ x 0j;tbþ offsetj;t þ ej;t ð4Þ

where h is the average degree of density dependence at the

stratum level during the breeding season (as in Eq. 2) and

the b0, j parameters are stratum-specific growth rates

(analogous to r from Eq. 2). These growth rates areadjusted by b, the vector of parameters to be estimated

for xj,t, the vector of potentially time-varying and

spatially explicit covariates. The b parameters thusdirectly add to or subtract from the population dynamics

in each stratum when covariate values differ from 0. A

population exhibits density dependence when h , 1, apositive association with population density when h . 1,

and density independence when h¼1 (Dennis et al. 2006).

Unstructured (e), spatial (e j), temporal (et), or spatio-temporal (e j,t) stochasticity was modeled with random

effects e ; N(0, r2) (for greater detail, see Ross et al.

2012). An offset term was incorporated into the model toaccount for differences in the number of segments

sampled in each stratum in each year. For a given year

in a given stratum, offsetj,t was the logþ 1 of the numberof segments sampled minus the minimum number of

segments ever sampled in stratum j.

To estimate the multiple processes that could have

affected scaup population dynamics in the NWT duringa .50 year time span, and to formalize our hypotheses

about the underlying mechanisms affecting scaup

population dynamics, we arranged covariates into threegroups: (1) density dependence, (2) climate, and (3)

predation. Models were then compared using the

negative mean of the log of conditional predictiveordinate (CPO) values, �(Rlog(CPOj,t)/sample size);

Held et al. (2010). The CPO uses a form of leave-one-

out cross-validation to calculate the probability of eachobservation (yj,t) when the model is fit without that

observation. The summary statistic of these CPO values

then provides a method to rank various models based ontheir predictive ability (Hooten and Hobbs 2015). A

lower summary statistic of CPO values simply indicates

that a model is better at predicting observations relative

to another; there is no theory indicating that a differenceof 1 in the statistic between models is inferentially better

than a difference of 0.5, for example. We then combined

variables from the best models of each group (i.e., lowestCPO value) to simultaneously quantify effects of density

dependence, climate, and predation.

Density-dependent effects

We chose the Gompertz form of density dependence

because it performs well in population dynamics studies

of waterfowl (Sæther et al. 2008) and other species

(Dennis et al. 2006, Knape and de Valpine 2012; Eq. 1),

and because it is difficult to statistically identify

alternative models for density dependence from one

another (Dennis and Taper 1994), although the func-

tional form of density dependence can be important for

management decisions (Runge and Johnson 2002). In

addition, the estimated intensity of density dependence

can be biased when studies fail to separate sampling and

process error, leading to incorrect conclusions about the

role of density dependence in a system (Freckleton et al.

2006). We therefore used hierarchical models to separate

sampling and process error and reduce bias in the

estimation of key focal parameters, such as density

dependence and other drivers of population perfor-

mance (de Valpine and Hastings 2002, Knape and de

Valpine 2012). We estimated density dependence using

the entire duration of the study from 1957 to 2012 in

order to gain insight into the strength of density

dependence in the absence of covariates. We also used

this same time period to determine which random effects

to include in the process model (i.e., spatial, temporal,

spatiotemporal, or unstructured error) and which data

model to use for further models (i.e., the negative

binomial or zero-inflated negative binomial).

Climate effects

Scaup arrive on the breeding grounds and nest later

than many other waterfowl species (Austin et al. 1998).

Because this unique life history characteristic offers little

opportunity for renesting after failure (Afton 1984),

scaup may be especially sensitive to environmental

changes. To examine how climate impacts scaup

population dynamics in the NWT, we considered an

array of climate variables that could affect environmen-

tal conditions for scaup on their breeding grounds.

These included broad-scale climate circulation indices as

well as more fine-scale variables. Each chosen climate

variable had previously been shown to affect the

population dynamics of aquatic birds (Papineau 2001,

Drever et al. 2012, Smith and Gaston 2012). Because of

differences in data availability, we quantified the effects

of climate for two time periods: 1967–2010, the time

period when snow extent data were available, and 1958–

2010, the time period when all other climate variables

were available. Unless otherwise stated, each covariate

was averaged over the current ‘‘scaup year,’’ from the

beginning of June in year t� 1 to the end of May in year

t (because the BPOP survey in the NWT tends to occur

in early June each year). We chose this time frame to

incorporate possible effects of environmental conditions

and trophic mismatches (Drever et al. 2012) on duckling

survival from year t� 1 to year t when populations are

counted. We also considered lag-1 effects for climate

variables on the breeding grounds because climate

during June t � 2 to May t � 1 can affect primary

productivity and the abundance of alternate prey, e.g.,

microtine rodents for foxes (Elmhagen et al. 2000) and


fish for mink (Zschille et al. 2014), potentially eliciting a

numerical response in predators that could in turn affect

waterfowl nest success and offspring survival in the

following year (Walker et al. 2013). To help with

convergence, we standardized climatic variables over all

strata to a mean of 0 and variance of 1 from the period

1958–2010, except snow cover extent, which was

standardized to a mean of 0 and variance of 1 from

the period 1968–2010 due to a lack of data prior to 1968.

In addition to the broad-scale Arctic Oscillation (AO)

and Pacific Decadal Oscillation (PDO) circulation

indices that could influence overall wetland dynamics

and food resources throughout the NWT (Papineau

2001, Morrison and Hik 2007, Smith and Gaston 2012),

we also considered more fine-scale climate variables to

gain deeper insight into spatiotemporal processes.

Palmer Drought Severity Index (PDSI) data were

available in a 2.5-degree grid over the study area (Dai

et al. 2004). The center of each stratum was calculated,

and the grid value that corresponded to this center was

used as an estimate for the stratum. Rather than

calculate PDSI for the entire scaup year, we used

specific time periods related to the time of breeding as

the covariate. We calculated PDSI for the following

three seasons: early (the months of May just before t� 1

and June of year t� 1), late (July and August of year t�1), and total breeding season (the month of May just

before t� 1 through August of year t� 1). The response

of scaup to PDSI during the breeding season would then

affect surveyed abundance in year t. The lag-1 effects of

PDSI were calculated in the same fashion but relative to

year t � 2, which could capture complex trophic

interactions among PDSI, alternative prey, and preda-

tors that eventually affect scaup.

The spring melt of winter snowpack may have a

greater effect on wetland dynamics than other forms of

precipitation, and decreased snow cover duration has a

negative impact on scaup abundance (Drever et al.

2012). Here, we averaged snow cover extent, or the

percentage of land covered by snow in a given grid cell,

over the current scaup year from June of year t � 1 to

May of year t. Data on snow cover extent were in a grid-

based format (Robinson and Frei 2000) and aligned in

the same manner as the PDSI data. The measure of

snow cover extent in the current scaup year would affect

surveyed abundance at time t in stratum j primarily

through settling and habitat selection decisions (e.g.,

through wetland and icepack conditions upon arrival to

the breeding grounds). The lagged effect would be

indicative of impacts on demography in the previous

breeding season that, in turn, affect surveyed abundance

at time t. Thus, to capture any impacts snow extent

might have on complex trophic interactions that take

time to percolate through the food web to scaup, we also

considered lag-2 effects.

We chose the climatic indices just described for their

relationship to high latitudes and boreal forest habitat.

Changes in climate along migratory routes could have a

direct impact on migratory phenology, and because the

BPOP survey is not designed for the scaup life cycle,

such processes could, in turn, affect the abundance of

scaup counted on the breeding grounds (i.e., through an

availability bias; Austin et al. 2002). To account for such

processes to the best of our abilities, we used the El Nino

Southern Oscillation (ENSO) and the abundance of

ponds in the prairies in the current scaup year as

covariates because each might affect the availability of

habitat and food resources during scaup migration

northward to the NWT (Naugle et al. 2000, Stenseth et

al. 2003). However, we note that changes in migratory

phenology could also be affected by other variables that

are difficult to measure at broad scales.

Predator effects

We also evaluated the relationship between scaup

population dynamics and indices of predator abun-

dance: red fox, Vulpes vulpes, total fox (red and Arctic

fox, V. lagopus), and mink, Neovison vison, which are

known to prey heavily on scaup nests, ducklings (Talent

et al. 1983, Pietz et al. 2003), and reproductive females

(Afton 1984, Koons and Rotella 2003). An index to

predator abundance for each species, or group of

species, was developed based on furbearer data from

Statistics Canada for 1958–2012. The number of

furbearer pelts harvested was reported collectively for

the Northwest and Nunavut territories until 1999 (when

the territories divided). To estimate the proportion of

fox pelts harvested in the boundaries of the current

NWT alone until 1999, we calculated the average

proportion of pelts harvested from each territory using

data available from the period 2000–2006. The propor-

tion of fox pelts harvested from the NWT during 2000–

2006 was applied to past data to obtain estimates of the

fox pelts harvested in the NWT during 1970–1999.

Because nearly all mink (.90%) were collected within

the current NWT border, and not Nunavut, no

proportional adjustment was made for the mink data

and the collective counts were used.

Because furbearer harvest could easily be influenced by

socioeconomic factors related to fur trapping, we first

used the price per pelt adjusted for inflation and the lag-1

adjusted price per pelt as predictor variables in a linear

regression model for furbearer abundance, because

furbearer harvest comprises the best available data for

predators in the NWT (Elton and Nicholson 1942, Yan et

al. 2013). All models were fit using maximum likelihood.

The best model for socioeconomic drivers of annual pelt

numbers was selected using Akaike’s information crite-

rion adjusted for sample size, AICc (Akaike 1973). The

standardized residuals from the best model for each

predator species were then used as a covariate in the

process model for scaup population dynamics for 1958–

2012 (Eq. 4), with the residuals in fall and winter of year t

� 2 affecting scaup abundance in year t (e.g., fox

abundance in 2000 would affect recruitment of scaup in

2001, the effects of which would be seen during the 2002


survey; noting that pelts harvested in late winter would be

tallied in the 2000 furbearer harvest statistic).

Model implementation

We then considered additive and plausible interactive

models with the variables that performed best in thepreceding topical analyses. Typically, the state-space

model previously described (Eqs. 3 and 4), with orwithout covariates, would be fit using Markov chainMonte Carlo estimation of posterior distributions,

usually using a combined Gibbs sampler and Metrop-olis-Hastings algorithm after solving for the full-

conditional distributions where closed-form solutionsexist (Banerjee et al. 2004). Instead, we used integrated

nested Laplace approximation (INLA) to approximatethe marginal posterior distributions of the parameters of

interest (Rue et al. 2009, Ruiz-Cardenas et al. 2012). Bymaking use of latent Gaussian models, INLA is capable

of approximating the posterior distribution with highaccuracy at a much faster computational rate than

Markov chain Monte Carlo estimation of posteriordistributions of the parameters (Rue et al. 2009). We

implemented INLA using the R package (Rue et al.2009, R Core Team 2013), and provide annotated code

pertaining to our best combined model from the period1967–2010 in the Supplement. Priors were set using

default values and distributions in the INLA package(Rue et al. 2009, Ruiz-Cardenas et al. 2012). Additionalbackground on a related model and implementation can

be found in previous work (Ross et al. 2012).

RESULTS

Density-dependent effects

The strength of density dependence was significant (h¼0.7904 6 0.05; all values reported as mean 6 SD) whenimplemented in a model without covariates for climate or

predator abundance. We thus considered density depen-dence in further models with climate and predator

covariates because the effect of density dependence canchange in the presence of environmental variability and

resource limitation (Viljugrein et al. 2005). A processmodel with an unstructured random effect (e) was theonly form of random effect that converged for all models

and was used in subsequent models with climate andpredator covariates, along with a negative binomial data

model (�(Rlog(CPOj,t)/sample size) of 5.040 vs. a zero-inflated model, 5.043). The zero-inflation parameter (w)in the zero-inflated negative binomial model was 0.00306 0.0028. The relatively small value of w provides

additional support for using the simpler negativebinomial model in subsequent models.

Climate effects

When we compared climate effect models for 1967–2010 (when snow extent data were available) using the

�(Rlog(CPOj,t)/sample size), a model with an immediateeffect of snow cover extent ranked better than models

with other effects of snow extent, as well as models with

AO, PDO, and PDSI covariates, although a model with

lag-1 July–August PDSI ranked second best (Appendix:

Table A1). The lowest �(Rlog(CPOj,t)/sample size)

indicates that snow cover extent in the winter and

spring immediately preceding surveyed abundance at

time t was better at predicting scaup population

dynamics than other covariates, although a model with

a lag-2 effect was closely ranked. When eliminating

snow extent from the analysis and expanding the time

frame to 1958–2010, a model with a lag-1 effect of July

to August PDSI ranked best (Appendix: Table A2),

indicating that drought severity during the late breeding

season better predicts changes in scaup population

dynamics than other climate covariates available during

the 1958–2010 time period. The models with climate and

habitat covariates hypothesized to influence scaup

population dynamics in the NWT through changes in

migratory phenology (ENSO and pond counts) were not

well supported in either analysis (i.e., they performed

worse than models with more localized climate on the

breeding grounds).

Predator effects

The best socioeconomic model from the set of

furbearer regressions included a linear effect for the

price of pelts in the previous year for red fox and total

fox, and a quadratic effect of price of pelts in the current

year for mink (Appendix: Tables A3–A5). Residuals

from these models were z-standardized and used as

covariates in the process model for scaup population

dynamics.

In the group of models for predator index effects on

scaup population dynamics, all covariates performed

worse than a model with only density dependence

(Appendix: Table A6); however, in order to better

understand how predation may interact with climate to

affect scaup population dynamics, we included total fox

abundance and red fox abundance in the models with

combined effects.

Combined effects

For both time periods (1958–2010 and 1967–2010),

models with covariates related to local climate (July–

August PDSI þ lag-1 July–August PDSI, lag-1 July–

August PDSI only, snow cover þ lag-2 snow cover

extent or snow cover extent only, respectively) were

retained in the models among those allowing for various

combinations of the density dependence, climate, and

predator variables that performed best in the preceding

analyses. For the 1958–2010 time period, interactions

between an effect of total fox abundance and the

immediate and lagged effects of July–August PDSI were

additionally supported by the CPO summary statistic

(Tables 1 and 2). The interactive effect indicated that

during times of drought (i.e., negative values of lag-1

PDSI), the abundance of scaup pairs increased when the

index of total fox abundance was high. During wet

conditions with lag-1 PDSI, however, the highest levels


of scaup abundance occurred when the index to total fox

abundance was low (Fig. 3). The opposite relationship

was true for PDSI with no lag effect; scaup abundance

was lowest during wet conditions (high PDSI) and high

total fox abundance, and was high during drought

conditions and low total fox abundance (Fig. 3).

A much simpler model with only the immediate effect

of snow cover extent performed best for 1967–2010

(Table 3). An increase in the time-averaged snow cover

in the winter and spring immediately preceding surveys

at time t resulted in statistical and biologically significant

increases in scaup population abundance in a given

stratum at the time of survey, and vice versa (Table 4,

Fig. 4). All estimates of the growth rate for each stratum

from the top models (b0, j, Eq. 4) were greater than 0,

indicating an increasing population in each stratum at

covariate levels of 0 (Tables 2 and 4, Fig. 5). When

considered simultaneously with climate (e.g., snow: h ¼0.76 6 0.06), predator effects (e.g., total fox, 1967–2010:

h ¼ 0.79 6 0.06), or both (e.g., snow, lag-2 snow, plus

total fox: h ¼ 0.73 6 0.06), density dependence was

present during both time periods (Tables 2 and 4). The

overdispersion parameter in the negative binomial data

model was 12.13 6 1.89 for the July–August PDSIþ lag-

1 July–August PDSI model and 13.15 6 2.05 for the

snow model, indicating little overdispersion in the data

relative to lj,t.

DISCUSSION

Several studies have evaluated the effects of predation

(Sargeant et al. 1984, Beauchamp et al. 1996) and

abiotic drivers (Almaraz et al. 2012, Drever et al. 2012)

on waterfowl population dynamics, yet none that we are

aware of have simultaneously evaluated predation and

climatic effects and how they may interact. We show

that breeding pair dynamics of scaup in the Northwest

Territories were correlated significantly with climatic

variables, and our results suggest that the effects of

predation may shift with climate intensity (i.e., drought).

For the years when snow data were available, time-

averaged snow cover extent from the winter and spring

prior to the beginning of the breeding season in May of

year t was the most important climatic variable. The

importance of snow cover seems to primarily relate to

the immediate effects of snow cover, which probably

affect subsequent wetland conditions and scaup settling

decisions, as well as breeding propensity (Afton 1984),

as they arrive in the NWT, and less through trophic

TABLE 1. Comparison of models, ranked by the negative meanof the log of the conditional predictive ordinate (CPO)values, from the combined analysis of scaup (Aythya spp.)pair abundance in the Northwest Territories, Canada, 1958–2010.

Model �

PlogðCPOj;tÞ

sample size

Total fox 3 (PDSI þ PDSIlag-1) 5.0387PDSIlag-1 5.0409Total fox þ PDSIlag-1 5.0414PDSI þ PDSIlag-1 5.0414Total fox 3 PDSIlag-1 5.0416Total fox þ PDSI þ PDSIlag-1 5.0416Red fox þ PDSI þ PDSIlag-1 5.0424Total fox 5.0462Red fox 3 (PDSI þ PDSIlag-1) 5.0462Null 5.0463Red fox 5.0483

Notes: Covariates from the top models within each groupare abbreviated as Total fox and Red fox for the predatorgroup (a model with total fox or red fox, respectively) and thePalmer Drought Severity Index, PDSI and PDSIlag-1 for theclimatic group (a model with an effect of only lag-1 July–August PDSI or a model with an effect of July–August PDSIand lag-1 July–August PDSI). Null indicates a model with nocovariates, but all models contain an unstructured randomeffect and Gompertz form of density dependence in the processmodel.

TABLE 2. Parameter estimates from the top model shown in Table 1 for the combined analysis ofscaup pair abundance in the Northwest Territories, 1958–2010, including mean, standarddeviation, and 90% and 95% credible intervals (shown as quantiles).

Parameter Mean SD0.025

quantile0.05

quantile0.95

quantile0.975

quantile

b0,13 0.6554 0.19 0.2868 0.3039 0.9721 0.9936b0,14 0.8862 0.20 0.3715 0.4038 1.3322 1.3686b0,15 0.6089 0.28 0.2579 0.2812 0.9139 0.9412b0,16 0.6128 0.19 0.2581 0.2772 0.9186 0.9414b0,17 0.7493 0.23 0.3209 0.3488 1.1206 1.1525b0,18 0.6693 0.21 0.2828 0.2988 1.0016 1.0226PDSI �0.0083 0.01 �0.0311 �0.0274 0.0109 0.0146PDSIlag-1 0.0172 0.01 �0.0060 �0.0023 0.0366 0.0404Fox 0.0108 0.02 �0.0249 �0.0190 0.0406 0.0465PDSI 3 Fox 0.0192 0.01 �0.0027 0.0009 0.0374 0.0409PDSIlag-1 3 Fox �0.0196 0.01 �0.407 �0.0374 �0.0018 0.0016h 0.8474 0.05 0.7540 0.7689 0.9268 0.9422Offset �0.9790 0.02 �1.0157 �1.0102 �0.9454 �0.9386

Notes: The b0, j parameters represent the stratum-specific ( jth) growth rates, Fox represent thebeta estimates for the index of total fox abundance, PDSI represents the beta estimate for July–August PDSI, PDSIlag-1 represents the beta estimate for the lag-1 July–August PDSI, h representsthe strength of density dependence, and Offset represents the offsetj,t parameter related to thenumber of segments surveyed in each stratum and year.


effects related to resources and alternative prey for

predators. Additionally, this immediate effect of snow

cover extent on surveyed abundance may simply be

related to a systematic shift of migration timing by

scaup, and the timing of the survey may be too early to

adequately measure scaup abundance when such effects

are not accounted for. Future modeling efforts could

account for possible systematic observation errors like

these by using covariates in the observation model

(rather than the process model), which was not possible

in the INLA package. Despite the possible confounding

with migration timing, other studies have similarly

shown a positive relationship with the ‘‘phenology of

snow cover duration’’ (Drever et al. 2012), indicating

that greater and prolonged snow cover may have

positive effects on wetland resources that eventually

percolate up the food web to positively affect scaup

demography.

Indeed, the intensity of seasonal drought in the NWT,

as measured by the PDSI, had important effects on

scaup population dynamics and additionally supported

our hypothesis that complex trophic interactions may

play an important role. The inclusion of these covariates

in the top model for 1958–2010 suggests that scaup

demography responds most strongly to changes in water

availability during the late breeding season, probably

through mechanisms affecting predation on ducklings

and food resources that could affect both duckling and

juvenile survival (Dawson et al. 2000, Walker and

Lindberg 2005). Although not the vital rates with the

greatest potential to affect population growth, changes

in scaup duckling and juvenile survival can have

important impacts on population dynamics (Koons et

al. 2006). Additionally, the interaction of PDSI and

predators also suggests that scaup population growth is

highest when water conditions are best (high PDSI) and

predators are low, probably due to a release from

predation pressure and improved water quality. An

increase in scaup abundance with higher fox abundance

during drought conditions is likely to be tied to

FIG. 3. The interactive effect of the Palmer Drought Severity Index (PDSI) for (A) the lag-1 July–August PDSI and (B) theJuly–August PDSI with the index for total fox abundance on predicted change in the abundance of scaup pairs, Nt� Nt�1 withinthe surveyed area of stratum 13 (relationships hold for Strata 14–18). The surface is specified for predictions across 90% of therange of lag-1 July–August PDSI, July–August PDSI, and total fox abundance. Only the b0,13 parameter (the stratum-specificgrowth rate for stratum 13) plus the values of PDSI and total fox were used to calculate the change in abundance (i.e., densitydependence and stochasticity were ignored in depicting the covariate impacts on population growth). Black circles representobserved values.

TABLE 3. Comparison of models, ranked by the negative meanof the log of the CPO values, from the combined analysis ofscaup pair abundance in the Northwest Territories, 1967–2010.

Model �

PlogðCPOj;tÞ

sample size

Snow 4.9883Snow þ snowlag-2 4.9889Total fox 3 snow 4.9939Total fox þ snow 4.9948Total fox þ snow þ snowlag-2 4.9952Total fox 3 (snow þ snowlag-2) 4.9964Red fox þ snow þ snowlag-2 5.0017Red fox 3 (snow þ snowlag-2) 5.0107Null 5.0238Red fox 5.0250Total fox 5.0327Total fox þ snowlag-2 5.0409

Notes: Covariates from the top models within each group areabbreviated as Total fox and Red fox for the predator group (amodel with total fox or red fox, respectively) and Snow andSnowlag-2 for the climatic group (model just an immediate effectof snow cover extent or a model with an immediate and lag-2effect of snow cover extent). Null indicates a model with nocovariates, but all models contain an unstructured randomeffect and Gompertz form of density dependence in the processmodel.


alternative prey through the lag-1 PDSI, becausepredators are likely to focus on primary prey species

during times of decreased environmental quality. Atrophic interaction between water conditions, alternative

prey, predators, and scaup is also possibly supported bythe interaction between PDSI (with no lag effect) andpredator abundance. Scaup abundance is highest when

PDSI is highest and predator abundance is high, and islowest during drought conditions with low predator

abundance. The contrast between lag-1 PDSI and PDSIcould be because alternative prey species have not yetnumerically responded to increased primary productiv-

ity in wetland areas. As is the case with all statisticalextrapolations, our inference is conditional on the ability

of the model to accurately represent the true system.Thus, as usual, we must simultaneously interpret our

predictions with caution while acknowledging the valueof the scientific components in the model.Although correlative and not conclusive, our findings

suggest that more detailed studies of the interactiveeffects among climate, predators, and alternative prey

on scaup are needed. We advise some caution wheninterpreting our results because we were unable tocontrol for trapping effort (e.g., through license sales) in

the NWT when measuring residual indices of predatorabundance. Our measures could thus be poor indices of

actual predator abundance. As more detailed databecome available (e.g., age-structured predator harvest),

population reconstruction techniques (e.g., integratedpopulation models) could be used to better estimatepredator abundance.

The southern (ENSO) climate oscillation index was apoor predictor of scaup dynamics in the Northwest

Territories, as were fluctuations in pond counts in thePPR. Some researchers have hypothesized that scaup

may have changed their timing of migration (Austin etal. 2002), which could be related to variation intemperature on their early-spring staging areas (Naugle

et al. 2000). The lack of an ENSO effect on counts ofscaup pairs in the Northwest Territories suggests that if

such changes have occurred, they are not related to the

ENSO averaged over the scaup year as we had

hypothesized. In addition, changes in wetland numbers

in the PPR driven by drought, drainage, or tiling that

creates deeper wetlands (which in turn support fish that

compete with scaup for food resources) could affect

forage availability in this important staging area for

scaup migrating northward to the boreal forest (Anteau

and Afton 2006, 2008). The Spring Condition Hypoth-

esis (Afton and Anderson 2001, Anteau and Afton 2004,

2008) proposes that scaup may be migrating later

because of (1) insufficient food resources on the critical

prairie pothole region staging area, or (2) the need to

regain body condition during staging because of

insufficient food resources and body condition in more

southern locales, in turn resulting in fewer scaup arriving

on the breeding grounds in time to be counted, and

potentially affecting their demographic performance as

well (Anteau and Afton 2006). If this process is

occurring, variation in the PPR wetland numbers does

FIG. 4. The change in scaup pair abundance, Nt � Nt�1,with changes in the mean (solid line) snow cover extent betweenwinter and spring in the season immediately prior to the BPOPwaterfowl survey in year t within the surveyed area of stratum13 in year t (relationships hold for strata 14–18), along with95% credible intervals (dotted lines). Only the b0,13 parameterplus the values of snow were used to calculate the change inabundance (i.e., density dependence and stochasticity wereignored in depicting the covariate impacts on populationgrowth).

TABLE 4. Parameter estimates from the top model in the combined analysis of scaup pairabundance in the Northwest Territories, 1967–2010, shown in Table 3, including mean, standarddeviation, and 90% and 95% credible intervals (shown as quantiles).

Parameter Mean SD0.025

quantile0.05

quantile0.95

quantile0.975

quantile

b0,13 0.8044 0.23 0.3823 0.4186 1.1893 1.2296b0,14 0.8622 0.33 0.2471 0.3299 1.4119 1.5011b0,15 0.8480 0.24 0.3955 0.4522 1.2522 1.3141b0,16 0.8536 0.21 0.4331 0.4724 1.2343 1.2779b0,17 0.7940 0.26 0.2584 0.3328 1.2697 1.3507b0,18 0.9617 0.23 0.5144 0.5449 1.3719 1.4108Snow 0.1363 0.03 0.0703 0.0806 0.1934 0.2045h 0.7623 0.06 0.6494 0.6675 0.8569 0.8751Offset 0.1199 0.06 0.0181 0.0339 0.2072 0.2238

Notes: The b0, j parameters represent the stratum-specific ( jth) growth rates, Snow represents thebeta estimates for snow in the winter and spring preceding scaup abundance surveys at time t, hrepresents the strength of density dependence, and Offset represents the offsetj,t parameter relatedto the number of segments surveyed in each stratum and year.


not appear to be a good surrogate for identifying such

cross-seasonal effects on scaup pairs in the boreal forest.We found no evidence for an effect of PPR pondconditions on scaup abundance farther north in the

NWT. However, snow cover extent has declined overtime (Fig. 5), and over the long term, scaup have looselytracked this decrease in snow cover extent. Only in the

most recent years is the pattern disparate, indicating thatsnow cover extent is not explaining everything. The

current trend in NWT scaup abundance, however, is inthe opposite direction (Fig. 5), indicating that thepopulation may not have been declining in the last

several years, despite the decrease in snow cover extent.Other long-term, large-scale studies of population

dynamics in waterfowl species (Viljugrein et al. 2005,Sæther et al. 2008, Murray et al. 2010) found marginalsupport for density dependence in diving ducks,

including scaup. Our results indicated that densitydependence on the breeding grounds is an importantdriver of scaup pair abundance, at least in the NWT. An

important aspect of our study was the reduction in biasby separately estimating sampling and process error

(Freckleton et al. 2006). Previous analyses we conductedthat did not properly account for this bias through state-space modeling yielded results suggesting that density

dependence was not an important driver of scauppopulation dynamics in the NWT (results not shown),highlighting the importance of this state-space modeling

approach. Although we did not explicitly test interac-tions between climatic variables and density dependence,

the strength and significance of density dependence didnot change with the inclusion of climate and predationeffects, and was a significant driver of population

dynamics with or without other covariates. Althoughour results are limited to inference on the breeding

grounds, density dependence could be affecting scaup

throughout their migratory cycle. Future studies will be

needed to isolate seasonality of density dependence inthe scaup life cycle, and how it affects populationdynamics through density-dependent competition for

food, predation of nests, increases in disease transmis-sion (Lima and Berryman 2006), or a combination offactors that requires further research targeted at

identifying density-dependent mechanisms.There are several ways in which our results can be

used to help guide management actions. For example,determining the relative influence of predation andclimate on population dynamics can fundamentally

change directives of management actions taken toinfluence a population most efficiently (e.g., predator

control during drought, habitat management, orbroader-scale policies directed at mitigating the im-pacts of climate change). Moreover, the effect of local

density dependence on the breeding grounds indicatesthe potential for scaup to rebound following perturba-tions (e.g., through enhanced reproductive success),

and estimates of the strength of density dependence arecrucial for guiding harvest management. These pro-

cesses are of high management concern (Austin et al.2006) and deserve additional study using modern,quantitative methods that can take advantage of

available data. A better understanding of how densitydependence interacts with environmental processessuch as predation and climate is also the focus of

future research efforts, because INLA currently limitsthis analysis. Expanding the scale of this method to

incorporate the entire BPOP survey area could alsoprovide a better understanding of the interactive effectsof harvest and density dependence on scaup population

dynamics.In conclusion, changes in abundance of breeding

scaup in the NWT seems to be most greatly tied to

FIG. 5. Predicted number of scaup pairs (solid line with 95% credible interval in dotted lines), scaled snow cover extent instratum 13 (dashed line with cross), and observed number of scaup pairs (black circles) within the surveyed area of stratum 13 ofthe Northwest Territories, given all the estimated fixed and random effects of our top model presented in Table 4.


density dependence, climate, and, to some extent,

predator abundance, specifically an interaction between

predators and climate for some time periods. Scaup

population dynamics do not seem to be driven by

climate and pond conditions in the south, or at least are

not as good at predicting population changes as snow

cover extent and drought in the north. Exploration of

other variables that could be affecting migratory

phenology, and the potentially related effects on

surveyed counts, deserve further study. Our results

highlight the benefits of comparing multiple environ-

mental and intrinsic population drivers when studying

species of management and conservation concern to

determine how climatic indices may affect populations

through both direct and indirect pathways. Although

the results might not yet be clear enough to guide on-

the-ground management actions, our findings build

upon the work of Drever et al. (2012) and provide

insight into where future research on scaup population

dynamics should be conducted.

ACKNOWLEDGMENTS

Earlier drafts of the manuscript were improved withcomments by P. Adler, P. Budy, F. Howe, M. Pendergast, J.Powell, M. Runge, and S. Supp. Funding for B. E. Ross wasprovided by Delta Waterfowl. Reviews by T. Arnold and M.Runge improved the final manuscript. Any use of trade, firm, orproduct names is for descriptive purposes only and does notimply endorsement by the U.S. Government.

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SUPPLEMENTAL MATERIAL

Ecological Archives

The Appendix and the Supplement are available online: http://dx.doi.org/10.1890/14-0582.1.sm


http://dx.doi.org/10.1890/14-0582.1.sm

combined effects of climate, predation, and density

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